The Fluxional Calculus: An Elementary Treatise ...Baldwin, Cradock and Joy, 1826 |
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Página v
... fluent Series for the computation of logarithms Briggs's method Borda's ditto Haros ' ditto De Moivre's formula Imaginary functions Series for the sine and cosine of the multiple arc Imaginary logarithmick and circular expressions ...
... fluent Series for the computation of logarithms Briggs's method Borda's ditto Haros ' ditto De Moivre's formula Imaginary functions Series for the sine and cosine of the multiple arc Imaginary logarithmick and circular expressions ...
Página 36
... fluent of a given fluxion . If it were required to give a definition of the fluent of a proposed fluxion , we must suppose that two fluxions are under consideration , and their fluents may be defined to be two magnitudes , the limiting ...
... fluent of a given fluxion . If it were required to give a definition of the fluent of a proposed fluxion , we must suppose that two fluxions are under consideration , and their fluents may be defined to be two magnitudes , the limiting ...
Página 37
... fluent may sometimes be determined at once from inspection . The fluxion of x3 being 3x2dx , the fluent of 3x dx must be a3 . Also , since d.x + 1 = m + 1 . xmdr , therefore f.m + 1 xmdx = x2 + i . Upon the same principle Л ( ydx + xdy ) ...
... fluent may sometimes be determined at once from inspection . The fluxion of x3 being 3x2dx , the fluent of 3x dx must be a3 . Also , since d.x + 1 = m + 1 . xmdr , therefore f.m + 1 xmdx = x2 + i . Upon the same principle Л ( ydx + xdy ) ...
Página 38
... fluent has been corrected , and a particular value assigned to the variable . 9. The constant multiplier or divisor may be removed from under the symbol f For ( Art . 12. ) d.ax = adx , therefore fadx = afdx . 1 Hence fodx = m + 1 · Sm ...
... fluent has been corrected , and a particular value assigned to the variable . 9. The constant multiplier or divisor may be removed from under the symbol f For ( Art . 12. ) d.ax = adx , therefore fadx = afdx . 1 Hence fodx = m + 1 · Sm ...
Página 40
... fluent and suppose x = b when u = 0 , we have xm + 1 u = + c m + 1 bm +1 and 0 = m + 1 + C , xm + 1_fm + 1 ..u = m + 1 ; in which expression , if we substitute m = 1 , the result is น = 0 · This will be explained Chap . 5 . 15. RULE 2 ...
... fluent and suppose x = b when u = 0 , we have xm + 1 u = + c m + 1 bm +1 and 0 = m + 1 + C , xm + 1_fm + 1 ..u = m + 1 ; in which expression , if we substitute m = 1 , the result is น = 0 · This will be explained Chap . 5 . 15. RULE 2 ...
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Términos y frases comunes
absc abscissa assume asymptote axis bx² centre circle co-ordinates conjugate point consequently cos.x curvature curve cusp d³u differentiating draw dx dx dx dy dx² dxdy dy dx dy dy ellipse equal F(x+h finite fluent fluxional coefficients fluxional equations function given point hence hyperbola hyperbolick increment infinite inflexion integrated intersection latus rectum limit logarithms maxima and minima maximum minimum negative ordinate origin parabola parallel partial fluxions perpendicular polar equation positive radius ratio required equation right angles right line sin.x sine solid spiral substitution subtangent suppose supposition surface tangent plane Taylor's theorem vanish variables velocity vertex whence xn+1
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Página 241 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.
Página 17 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 32 - Ultimae rationes illae quibuscum quantitates evanescunt, revera non sunt rationes quantitatum ultimarum, sed limites ad quos quantitatum sine limite decrescentium rationes semper appropinquant, & quas propius assequi possunt quam pro data quavis differentia, nunquam vero transgredi, neque prius attingere quam quantitates diminuuntur in infinitum.
Página 32 - By the philosophical use of words, I mean such an use of them as may serve to convey the precise notions of things, and to express, in general propositions, certain and undoubted truths which the mind may rest upon and be satisfied with, in its search after true knowledge.
Página 229 - ... positions in which it will rest in equilibrium. 13. A machine, driven by the impulse of a stream, produces the greatest effect when the wheel moves with one-third of the velocity of the water. 14. At a place whose latitude is 48°. 50'. 14", the meridian altitude of the spn's upper limb was observed to be 62°. 29'.
Página 32 - By their civil use, I mean such a communication of thoughts and ideas by words as may serve for the upholding common conversation and commerce about the ordinary affairs and conveniences of civil life, in the societies of men one amongst another.
Página 226 - A known weight (P) at the extremity of a rod which passes through two small rings fixed in the same vertical line, by its pressure puts a solid inclined plane in motion along an horizontal table; given the weight of the plane, find its elevation sothatthe velocity communicated to it in a given time may be a maximum.
Página 60 - The sines and cosines of multiple arcs may also be developed in terms of the powers of the sine and cosine of the simple arc, by help of a remarkable formula, known by the name of De Moivre's formula, which may be easily established, as follows.
Página 17 - The logarithms of the same number in different systems are to each other as the moduli of those systems. This is evident from the general logarithmic series. Thus the logarithm of 1 + x in a system whose modulus is m...
Página ii - Angli, nomine magis idoneo, quantitates fluentes vocant, et earum incrementa infinite parva seu evanescentia fluxiones nominant, ita ut fluxiones ipsis idem sint, quod nobis differentialia. Haec diversitas loquendi ita jam usu invaluit, ut conciliatio vix unquam sit expectanda : equidem Anglos in formulis loquendi lubenter imitarer, sed signa, quibus nos utimur, illorum signis longe anteferenda videntur.